Over time, a population acquires neutral genetic substitutions as a consequence of random
drift. A famous result in population genetics asserts that the rate, K, at which these substitutions
accumulate in the population coincides with the mutation rate, u, at which they arise in
individuals: K = u. This identity enables genetic sequence data to be used as a “molecular
clock” to estimate the timing of evolutionary events. While the molecular clock is known to
be perturbed by selection, it is thought that K = u holds very generally for neutral evolution.
Here we show that asymmetric spatial population structure can alter the molecular clock
rate for neutral mutations, leading to either K<u or K>u. Our results apply to a general class
of haploid, asexually reproducing, spatially structured populations. Deviations from K = u
occur because mutations arise unequally at different sites and have different probabilities of
fixation depending on where they arise. If birth rates are uniform across sites, then K u. In
general, K can take any value between 0 and Nu. Our model can be applied to a variety of
population structures. In one example, we investigate the accumulation of genetic mutations
in the small intestine. In another application, we analyze over 900 Twitter networks to
study the effect of network topology on the fixation of neutral innovations in social evolution.